Leaders of Germany’s Alternative für Deutschland have vowed to “take back our country and our people” and “hound Angela Merkel” with a legal investigation into the refugee crisis as they became the first overtly nationalist party to swoop into the Bundestag in more than five decades.

As the figures of the first exit polls flashed up on the screen shortly after 6pm on Sunday, supporters inside a Berlin nightclub hired by AfD broke out into a spontaneous rendition of the national anthem – though they made sure to skip the first two stanzas, still strongly associated with the Third Reich.

“Please, no remarks that will later come back to haunt us,” the party’s joint candidate Alexander Gauland quickly admonished the euphoric crowds from the stage.

Projected results put the AfD on 13%, behind Angela Merkel’s Christian Democrat-led alliance on 32.9% and the Social Democratic party on 20.8%. The rightwing populist party’s delegates are expected to take more than 80 out of 631 seats in the next parliament.

German elections 2017: latest results live

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While the result may not be on the scale of 52% of Britons voting to leave the European Union or 46% of US voters casting their ballot for Donald Trump, it nonetheless represents a landmark in postwar German history.

Germany’s rightwing populists will arrive in the Bundestag with the best result for any new party since 1949, a higher share of the vote than either the Greens or the leftwing Die Linke have achieved in several decades.

In the states that used to form East Germany, AfD looks likely to become the second-largest party.

AfD may not be the first far-right party to enter the Bundestag since the second world war: until 1960 a number of small nationalist groups took part in the coalition government under West Germany’s first post-war chancellor, Konrad Adenauer.

But it will be the first party with an overtly nationalist rhetoric and agenda to claim seats in Berlin’s Reichstag, a building that still echoes with the horrors of the Nazi era.

Among its members are figures such as the lawyer Jens Maier, who has called for an end of the “guilt cult” over the second world war; the head of the AfD youth wing, Markus Frohnmaier, who has vowed to make politics “for the volk and only for the volk”; and Lower Saxony’s Wilhelm von Gottberg, who has described the Holocaust as “an effective instrument to criminalise Germans and their history”.

Even the AfD’s head, Frauke Petry, once considered a firebrand in her own right but who has found herself marginalised and conspicuously missing from the grand party in Berlin, criticised her colleagues, saying they were putting off many middle-class voters. “I can understand why they are horrified,” she said.

Drinking a beer on the balcony of the nightclub the party had hired, Heribert Eisenhardt denied that the party has increasingly lurched to the right since its foundation in 2013, saying the developments had been misportrayed by the media. “I am not even proud to be German,” Eisenhardt said, waiting for the surprise on the faces of his party colleagues, only to add: “As long Angela Merkel is our chancellor.”

Many of his party colleagues teasingly smiled and waved at the several hundred protesters who had gathered at the bottom of their balcony. “My god, these people are braindead,” said one female supporter wearing an AfD pin on her dress. “Gulag may be a good solution.”

An hour earlier they had cheered on Gauland as he promised: “We will change this country … we will take back our country and our people.” His co-leader, Alice Weidel, vowed she would prioritise a parliamentary investigation into Merkel’s decision to open Germany’s borders during the 2015 refugee crisis.

Frauke Petry said her AfD colleagues were putting off many middle-class voters: ‘I can understand why they are horrified.’ Photograph: Alexander Hassenstein/Bongarts/Getty Images

Some critics question whether AfD will be able to take quite so smoothly to its new role inside the Bundestag. As in the US there is hope, and in some parts confidence, that AfD’s momentum will soon be stopped by constitutional safeguards and the slow grind of parliamentary procedure.

A new satirical video by the comedian Jan Böhmermann, called Deutschland ist Wieder im Reichstag (“Germany is back in the Reichstag”) imagines the party’s triumphalism being ground to a halt by endless budgetary reports and committee sessions: “Parliamentarianism can paralyse the raciest racism”, goes one line.

What the stunning success of AfD means for Germany and Europe | Cas Mudde

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Manfred Güllner, the director of the polling institute Forsa, predicted on the eve of the election that unresolved conflicts between the AfD’s nationalist and economically liberal wings would soon catch up with the party: “The AfD will take itself apart because that’s what has always happened to sectarian groups on the far right.”

Founded by a group of economics professors in protest against Greek bailout programmes, the party’s success in the east shows the extent to which it has broadened its appeal and has reached out to those who feel disappointed by their region’s decline after reunification.

Yet AfD is by no means only a party of the “left-behinds”, and its agenda continues to be set by western politicians advocating conventional small-state economics. A June survey showed that the largest part of the party’s supporters, 39%, have a higher than average income.

Its manifesto calls for a scrapping of inheritance tax and suggests that the long-term unemployed should do 30 hours of work a week below the minimum wage. Resolving the party’s contradictory stances on tax and pensions could soon dampen Sunday night’s triumphalism.